Why do multitap ballasts have more current on 120v than 208, 240, 277v? I was looking at a fixture on ebay, and the ballast on 120v is 3.8a. Why is that? Cause regular 120v HID ballasts have lower current than multitap HID ballasts.

According to Ohm's law, the current (amperes) and potential (volts) are inversely proportional at a given power (watts). This means the lower the voltage, the higher the current for the same power (wattage in this case). So a multi tap ballast will draw the most current at its lowest voltage, 120V in this case and the least at its highest voltage, probably 480V.

One of the main reasons why lighting circuits sometimes use higher voltages is because it requires less current. This means the diameter (gauge) of the wires can be smaller at higher voltages, which lessens the materials cost. With a higher voltage, longer runs will work better, too.

Maybe the question was meant: "Why a multitap ballast draws on 120V more current than a standard 120V only counterpart?"
The main difference between these two is, the multitap ballast has to fit into the primary bobbin windings for all tabs, the 120V only version has all that room available for only the 120V winding. That means the multitap has to use thinner wire for the primary. And a thinner wiremean higher resistance and that means hjgher losses. And higher losses means the multitap ballast consumes more power on its input. And more power means higher current.
Of course, all above assumes the multiap ballast isnt made bigger to offset the extra losses back. But it would then be quite heavier.
My guess is, most makers will make the multitap either the same size (common tooling) or only slightly bigger, just to keep the operating temperature within the limits. In either case the multitap will have on 120V higher losses than the 120V only counterpart. The thing is, the multitap ballasts are assumed to be used mainly with other voltages than the base 120V, so the performance at 120V is a bit neglected.